Long before Mandelbrot gave fractal geometry a name, mathematicians were grappling with the concepts related to the fractal dimension. While studying the coast of England in the first half of the 20th century, Lewis Fry Richardson realized that the smaller the ruler, the longer the coastline measurement would be. As your measuring tool decreases, it is able to capture more of the details of a jagged shape's outline. In fractal terms, the coastline of England is infinite. (iStockphoto.com/scibik)